Answer
The interval in which the avg. rate of change was most positive is 1999-2001, when the number of articles published increased at an average rate of $500$ articles per year.
Work Step by Step
The average rate of change of $f$ over the interval $[a, b]$ is given by:
Average rate of change of $f\displaystyle \ \ =\frac{f(b)-f(a)}{b-a}$
The units of the average rate of change of $f$ are units of $f(x)$ per unit of $x$.
In an excel worksheet (see image), calculate the average rate of change over $[3,5],[3,7],[11,13]$.
Highlighted is the cell with the most positive value.
Most positive value for the interval $[9,11]$ is:
$0.5$ thousand = $500$ articles per year.
The interval in which the avg. rate of change was most positive is 1999-2001, when the number of articles published increased at an average rate of $500$ articles per year.
